Quadratic diffusion Monte Carlo and pure estimators for atoms

Abstract

The implementation and reliability of a quadratic diffusion Monte Carlo method for the study of ground-state properties of atoms are discussed. We show in the simple yet non-trivial calculation of the binding energy of the Li atom that the method presented is effectively second-order in the time step. The fulfilment of the expected quadratic behavior relies on some basic requirements of the trial wave function used for importance sampling, in the context of the fixed-node approximation. Expectation values of radial operators are calculated by means of a pure estimation based on the forward walking methodology. It is shown that accurate results without extrapolation errors can be obtained with a pure algorithm that can be easily implemented in any previous diffusion Monte Carlo program.